Arsenal refuse to bow. This one had disaster stamped all over it as they entered with ranks depleted and stamina sapped following Saturday's FA Cup semi-final squeak past Wigan Athletic after extra-time and penalties. And it was possible to fear the worst for them when Matt Jarvis put West Ham United in front. Arsenal had laboured in the first-half and they knew that only a victory would do. It was no exaggeration to say that their Champions League hopes depended on it.

Yet they found the answers in something approaching the style of old. There were two goals from Lukas Podolski, each an unerring left-footed blast and with the first nicely timed on the point of half-time. West Ham pointed to that as the turning point. But it was Olivier Giroud who stole the show with a quite magnificent finish in between times.

Giroud has felt the Arsenal fans' frustrations of late, as the club's Premier League title challenge has given way to the more familiar fight for a top-four place. His performances have been substandard and his toils in the first half here did little to soothe the angst. As he missed a couple of chances, the second a shockingly timid flick when clean through, the nerves looked all too visible. Yet he put the tension aside on 55 minutes with a touch and finish that carried shades of Dennis Bergkamp and set Arsenal en route to what was, ultimately, a fairly stress-free win. It was Giroud's 20th goal of the season and it was difficult to recall any of the preceding 19 being as easy on the eye.

Arsenal jumped back to fourth, although the elevation could be short-lived, with Everton entertaining Crystal Palace on Wednesday night. The scrutiny is on the run-ins, with Arsenal noting that Everton must play the Manchester clubs and Southampton – their final fixtures look kinder. Arsène Wenger and his players, though, could simply content themselves with having done their job.

Arsenal had resembled a battalion of the walking wounded and it had been possible to count as many as 14 of their personnel that were either unavailable or pre-match doubts. Wenger could select Laurent Koscielny, Tomas Rosicky and Podolski in the end, while Aaron Ramsey appeared only as a substitute and Alex Oxlade-Chamberlain remained on the bench. West Ham were the fresher, having last played on the Sunday before last in the home defeat to Liverpool.

Wenger went for experience, with Giroud the youngest outfield player at 27 and the worry for Arsenal was whether they had enough pace. West Ham boasted more of it, which is not supposed to happen.

West Ham had chances before they scored and the shape of the game might have changed had Jarvis gone down under Bacary Sagna's 18th-minute swipe inside the penalty area. Jarvis stayed on his feet despite the illegal contract and the referee Kevin Friend did not blow for the penalty, which raised the question of whether the winger's honesty had done his team any favours. Sam Allardyce, the West Ham manager, was categoric it had not. Wenger admitted that he was grateful.

West Ham flickered in the first-half and it was no great surprise when they went ahead. Antonio Nocerino got in behind Kim Kallstrom and he forced Wojciech Szczesny to save. But when he worked the ball back, Jarvis put his head in front of Koscielny's high boot to head home.

Arsenal's response was immediate, which probably spared them a volley of half-time boos. They, too, had created chances, only for Giroud to fluff his lines – first when he could not connect with Podolski's whipped cross and then, more lamentably, with a weak effort from the busy Santi Cazorla's pass. However, after Kallstrom had forced a save out of Adrián, Arsenal dug out the equaliser. Stewart Downing's clearance found only Cazorla and his ball liberated Podolski, who rifled low into the far corner.

Arsenal needed inspiration in the second half and Giroud provided it as he ascended quickly to the status of hero. West Ham had cleared a corner and they appeared well covered when Thomas Vermaelen hoisted a high ball back into the area. The space for Giroud was minimal and the technique needed to be flawless. Happily for Arsenal, it was. The touch with the left foot to pull the ball out of the sky and tee up the shot was a moment of genius and the second, a thumping right-footer through the legs of Adrián, was not bad either.

Arsenal pressed for the third. Podolski drew a save from Adrián with a free-kick and Cazorla fizzed inches wide after a counter. They were much more composed and coherent after Giroud's goal and Podolski's second allowed them to coast to the end.